42ed5/2

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42ed5/2

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Prime factorization	2 × 3 × 7
Step size	37.7694¢
Octave	32\42ed5/2 (1208.62¢) (→16\21ed5/2)
Twelfth	50\42ed5/2 (1888.47¢) (→25\21ed5/2)
Consistency limit	2
Distinct consistency limit	2

42 equal divisions of 5/2 (abbreviated 42ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 42 equal parts of about 37.8⁠ ⁠¢ each. Each step represents a frequency ratio of (5/2)^1/42, or the 42nd root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	37.8
2	75.5	23/22, 24/23, 25/24
3	113.3	15/14
4	151.1	12/11, 25/23
5	188.8	19/17
6	226.6	25/22
7	264.4	7/6
8	302.2
9	339.9	17/14, 28/23
10	377.7
11	415.5	14/11, 19/15
12	453.2	13/10, 30/23
13	491
14	528.8	19/14, 23/17
15	566.5
16	604.3	17/12
17	642.1
18	679.8
19	717.6
20	755.4	17/11
21	793.2	19/12, 30/19
22	830.9	29/18
23	868.7	28/17
24	906.5	22/13
25	944.2	19/11
26	982	23/13, 30/17
27	1019.8
28	1057.5	24/13
29	1095.3
30	1133.1	23/12, 25/13
31	1170.9
32	1208.6
33	1246.4
34	1284.2
35	1321.9	15/7, 28/13
36	1359.7	11/5
37	1397.5
38	1435.2	23/10
39	1473	7/3
40	1510.8	12/5
41	1548.5
42	1586.3	5/2

Harmonics

Approximation of harmonics in 42ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.6	-13.5	+17.2	+8.6	-4.9	-7.4	-11.9	+10.8	+17.2	+3.3	+3.8
	Relative (%)	+22.8	-35.7	+45.6	+22.8	-12.9	-19.5	-31.5	+28.6	+45.6	+8.8	+9.9
Steps (reduced)		32 (32)	50 (8)	64 (22)	74 (32)	82 (40)	89 (5)	95 (11)	101 (17)	106 (22)	110 (26)	114 (30)

Approximation of harmonics in 42ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.3	+1.3	-4.9	-3.3	+5.1	-18.4	+1.4	-11.9	+16.9	+11.9	+10.5
	Relative (%)	+43.0	+3.4	-12.9	-8.7	+13.4	-48.6	+3.6	-31.5	+44.8	+31.6	+27.8
Steps (reduced)		118 (34)	121 (37)	124 (40)	127 (1)	130 (4)	132 (6)	135 (9)	137 (11)	140 (14)	142 (16)	144 (18)